1. Field of the Invention
The present invention relates to optical signal processing to determine features of a target optical spectrum, and, in particular, to the use of a chirped optical field to recover the target optical spectrum. Here a target optical spectrum is a spectrum at optical frequencies that is output by a device, included inherently in a material or device, or recorded by artificial action in a material or device, or formed in some combination.
2. Description of the Related Art
Information processing based on optical analog signal processing promises to provide advantages in speed, size and power over current information processing systems. Many versatile optical coherent transient (OCT) processing devices have been proposed. An OCT device relies on broadband complex spatial-spectral grating formed in the optical properties of a material, such as an inhomogeneously broadened transition (IBT) material, also called a spatial-spectral (S2) material. A spatial-spectral grating has the ability to generate a broadband optical output signal that depends on an optical probe waveform impinging on that grating and the one or more interacting optical signals that formed the grating.
In some OCT devices, the approach to accessing the information in the spatial-spectral grating is to probe that grating with a high bandwidth, Fourier-transform-limited optical signal, such as a coherent brief optical pulse, or a series of such coherent brief optical pulses. Under certain conditions, the probing of the grating can produce optical output signals that are generally referred to as stimulated photon echoes or optical coherent transients. A single brief coherent light pulse with a bandwidth equal to that of the spectral grating stimulates a time-delayed output signal whose temporal profile represents the Fourier transform of the spectrum recorded in the grating structure.
While useful in many applications, the approach of readout with a high bandwidth, Fourier-transform-limited coherent brief optical pulse or series of optical pulses at the full bandwidth of processing can suffer, at present, from the limited performance in dynamic range of photo-detectors and analog to digital converters (ADCs, also called digitizers) that are needed to make a measurement of any instantaneous high bandwidth optical signal. Existing high bandwidth detectors and ADCs have limited performance and higher cost as compared to lower bandwidth detectors and digitizers.
Swept frequency modulated optical signals are called “chirped optical fields” and “chirped laser fields” herein. The frequency sweep can be linear in time with a constant chirp rate (called linear chirp or linear frequency modulation, LFM) or non-linear with a time varying chirp rate. Optical LFM signals have been used as probe waveforms in pulse sequences to write spatial-spectral gratings for applications of storage, signal processing, true time delay generation, and arbitrary waveform generation, and also for readout of spectral gratings. LFM probe waveforms generate a temporal output signal that represents a collective readout of all the absorbers, as with the brief pulse excitation, but under the condition of swept excitation. By properly choosing the rate of frequency change with time, called herein the chirp rate κ, a temporal readout is produced that is slow enough to be digitized by low cost, high performance digitizers in the frequency bands of interest. See for example, published International Patent application WO 2003/098384 entitled “Techniques for processing high time-bandwidth signals using a material with inhomogeneously broadened absorption spectrum, Inventors: K. D. Merkel, Z. Cole, K. M. Rupavatharam, W. R. Babbitt, T. Chang and K. H. Wagner, 27 Nov. 2003 (hereinafter Merkel), the entire contents of which are hereby incorporated by reference as if fully set forth herein.
The concept of using a chirped laser field as a probe signal has been called spectral-to-temporal mapping. Coherent interaction of resonances of the physical system with the chirped laser field is called a stimulated photon echo or optical coherent transient effect. Commonly, this interaction results in a response signal that is a time varying change to the amplitude and/or phase of the probe field. The frequency sweep rate or chirp rate, κ, is defined as the frequency scan range, or bandwidth, B, divided by the duration of the sweep time, τc, as given by Expression 1aκ=B/τc,  (1a)
In some cases, the response field phase and amplitude can be directly observed. For some other cases, e.g., at optical frequencies, in order to obtain the full information about both the phase and the amplitude, a heterodyne detection scheme is used, where a reference field interferes with the response signal. Typically the reference field is close in frequency with the response signal so that a lower frequency beat output is produced that is readily observable with photo-detectors and high performance digitizers. Under some conditions, heterodyne detection is automatic, such as when the probe field spatially overlaps the response signal and acts as a reference, as in the case of absorption or dispersion. In other cases, the output signal is distinct from the probe field and a reference field is made to interfere with the response signal before being received by a measurement apparatus, such as a digitizing detector.
It has been observed that the detected signal received by the detectors is not a simple mapping in time of a target optical spectrum with which the probe signal interacts, but often includes spurious features. For example, an attenuated ringing of a single peak spectral feature in a target optical spectrum is observed in the detected signal. The composite ringing of multiple spectral features leads to a complex distortion of the target optical spectrum when mapped into a temporal readout signal.
A commonly used method to reduce the distortion to a negligible level is to limit the chirp rate to a slow sweep rate, usually set by an inequality such as in Expression 1bκ<<Γ2  (1b)Where Γ is the width of the finest spectral feature in the system. The use of a slow sweep rate to avoid distortion has been applied in various physical systems, such as acoustic systems, electric circuits, and optical systems.
For example, in optical absorption spectroscopy, the frequency swept excitation is widely used to directly map the absorption spectrum to the time domain; and the frequency chirped field is applied at a slow chirp rate to reduce the distortions, (S. P. Anokhow, V. I. Kravchenko, and M. S. Soskin, “Rapid spectroscopy using lasers with swept lasing frequency”, Opt. Spectrosc. 36(1), 10(1972)). Anokhow et. al. pointed out that “From the point of view of laser spectroscopy the most interesting mode of operation is adiabatically slow sweeping” and also that “Under adiabatically slow frequency sweeping the shape of the luminescence line does not have any appreciable effect on the kinetics, and the amplitude of the peaks results from the pumping intensity”. Duppen et. al. also observed the problem that using a fast chirp rate results in distortions, or asymmetrical ringing on the response in frequency chirped four wave mixing experiments (K. Duppen, F. de Haan, E. T. J. Nibbering, and D. A. Wiersma, “Chirped four-wave mixing”, Phys. Rev. A. 47, 5120(1993)). The sweep rate limit was also pointed out in the response of the frequency chirped excitation of a Fabry-Perot interferometer (M. J. Lawrence, B. Willke, M. E. Husman, E. K. Gusman, E. K. Gustafson, and R. L. Byer, J. Opt. Soc. Am. B, 16(4), 523(1999)). Optical frequency chirped fields have been used for readout of the spectral features in inhomogeneously broadened spectral materials. In the majority of such measurements, to map the spectral features to the temporal domain, the chirp rates were set to be slow with respect to the width of the finest spectral feature (C. M. Jefferson and A. J. Meixner, Chem. Phys. Lett. 189, 60(1992), A. J. Meixner, C. M. Jefferson, and R. M. Macfarlane, Phys. Rev. B 46, 5912(1992), Z. Cole, T. Bottger, R. K. Mohan, R. Reibel, W. R. Babbitt, R. L. Cone, and K. D. Merkel, Appl. Phys. Lett. 81, 3525(2002)). The entire contents of each of these references are hereby incorporated by reference as if fully set forth herein.
While a slow chirp rate can reduce such distortions, the use of a slow chirp rate is not always desirable or applicable. For example, a disadvantage of the slow chirp rate requirement is the need to know or accurately estimate the spectral resolution of the finest significant features in the spectrum of interest. Often the finest spectral resolution is not known. In some applications, the readout time is limited and a fast chirp rate (e.g., κ≧Γ2) is required to cover a sufficient bandwidth of interest.
For another example, in some applications of optical spectroscopy techniques, such as cavity ringdown absorption spectroscopy, which is a highly sensitive and accurate way to measure weak gas-phase molecular spectra, a fast chirp is required to enhance the performance. A swept-carrier frequency of the laser is used to observe the detected signal as the heterodyne beating between the transmitted field and the impulse response, and the distortions due to a fast frequency sweep are clearly observed.
In one approach, (Y. He, B. J. Orr, J. Chinese Chem. Soc, 48, 591(2001); Y. He, B. J. Orr, Appl. Phys. B75 267(2002); Y. He, B. J. Orr, Appl. Phys. B79, 941(2004)) subsequent steps were then taken to convert the temporal distortions into an envelope only function using a demodulating logarithmic amplifier, to observe the cavity ringdown time, but not to compensate for the distortions.
Based on the foregoing, there is a clear need for techniques to use a chirped optical field to probe a target optical spectrum, which does not suffer the deficiencies of prior art approaches to optical readout. In particular, there is a need for techniques to read out a target optical spectrum using chirp rates that are not limited by the finest spectral resolution of the target optical spectrum, which is not known in some applications.